Sparse reconstruction of brain circuits: Or, how to survive without a microscopic connectome

Inside one voxel of a cubic millimeter of neocortex, fifty to hundred thousand neurons use 4 km of axonal cable to form three to fifteen hundred million synapses with each other. While in the human, such voxel is a small fragment of a cortical area, in the mouse an entire cortical area, like the primary auditory cortex, can be contained in a voxel of this size. This raises the fundamental question of what happens inside such a voxel? Are the circuits contained in this voxel, and their operations, different in every area, or are there general principles that are conserved across cortical areas and species? Such questions go to the heart of understanding how the neocortex wires itself and works. One proposal is to answer these questions by mapping the entire circuit at synaptic resolution to produce a 'connectome' - of the cortical column, or even of the entire brain. However, such a high-resolution connectome is self-evidently unachievable with the tools available and as a strategy it still leaves us short of understanding the 'principles of neural engineering'. We offer an alternative route that uses physiology and computational modeling as a means of generating 'predictive anatomy', where the questions about underlying structure are directed to fundamental principles of organization and operation of the cortical circuits. This approach involves 'sparse' rather than 'dense' reconstructions at light and electron microscope resolution to keep the questions well-matched to current experimental tools. Rather than providing a snap-shot of an entire wiring diagram, our strategy provides for a statistical description of the circuit and integrates theory, function, and structure in a common framework.